Skip to main content
Springer Nature Link
Log in

A comparison of problem decomposition techniques for the FAP

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

This paper proposes a problem decomposition approach to solve hard Frequency Assignment Problem instances with standard meta-heuristics. The proposed technique aims to divide the initial problem into a number of easier subproblems, solve them and then recompose the partial solutions into one of the original problem. We consider the COST-259 MI-FAP instances and other Cardiff University test problems in order to simulate larger and more realistic networks. For both benchmarks the standard implementations of meta-heuristics do not generally produce a satisfactory performance within reasonable times of execution. However, the decomposed assignment approach can improve their results, both in terms of solution quality and runtime.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Aardal, K.I., van Hoesel, C.P.M., Jansen, B.: A branch-and-cut algorithm for the frequency assignment problem, R.M. 96\11 (1996)

  • Abbiw-Jackson, R., Golden, B., Raghavan, S., Wasil, E.: A divide-and-conquer local search heuristic for data visualization. Comput. Oper. Res. 33(11), 3070–3087 (2006)

    Article  MATH  Google Scholar 

  • Allen, S.M., Dunkin, N., Hurley, S., Smith, D.: Frequency assignment problems: benchmarks and lower bounds. University of Glamorgan (1998)

  • Angelsmark, O., Thapper, J.: Partitioning Based Algorithms for Some Colouring Problems. Lecture Notes in Computer Science, vol. 3978, pp. 44–58 (2006)

  • Beckmann, D., Killat, U.: Frequency planning with respect to interference minimization in cellular radio networks. Tech. Rep. 8th COST 259 Meeting, Vienna, Austria (1999)

  • Borovska, P.: Solving the travelling salesman problem in parallel by genetic algorithm on multicomputer cluster. In: Proc. of the International Conference on Computer Systems and Technologies CompSysTech’06, Veliko Tarnovo, Bulgaria, 2006

  • Brandes, U., Gaertler, M., Wagner, D.: Experiments on graph clustering algorithms. In: Proc. of the 11th Annual European Symposium on Algorithms, Budapest, 2003

  • Cardiff University Condor Pool. http://www.cardiff.ac.uk/insrv/it/condor/index.html, accessed on 1st June 2007

  • Cheng, C.B., Wang, K.P.: Solving a vehicle routing problem with time windows by a decomposition technique and a genetic algorithm. Expert Syst. Appl. 36(4), 7758–7763 (2009)

    Article  MathSciNet  Google Scholar 

  • Colombo, G.: A genetic algorithm for frequency assignment with problem decomposition. Int. J. Mob. Netw. Des. Innov. 1(2), 102–112 (2006)

    Article  Google Scholar 

  • Colombo, G., Allen, S.M.: Problem decomposition for minimum interference frequency assignment. In: Proc. of the 2007 IEEE Congress in Evolutionary Computation, Singapore, 2007

  • Colombo, G.: A decomposition approach for the frequency assignment problem. Ph.D. Thesis, Cardiff University, UK (2008)

  • Correia, L.M. (ed.): Wireless Flexible Personalised Communications. Wiley, Chichester (2001)

    Google Scholar 

  • Crainic, T.G., Toulouse, M.: Parallel Strategies for Meta-heuristic. State-of-the-Art Handbook in Metaheuristics, edited by Glover, F., Kochenberger, G., Kluwer Academic, Dordrecht (2002)

    Google Scholar 

  • Crompton, W., Hurley, W.S., Stephens, N.M.: A parallel genetic algorithm for frequency assignment problems. In: Proc. of the IMAC-IEEE Conference on Signal Processing, Robotics and Neural Networks, Lille, France, 1994

  • Eisenblatter, A.: Frequency assignment in GSM networks: Models, heuristics, and lower bounds. Ph.D. Thesis, Technische Universitat Berlin, Berlin, Germany (2001)

  • FAP web—A website about Frequency Assignment Problems. http://fap.zib.de/, accessed on 1st June 2007

  • Gendreau, M., Guertin, F., Potvin, J.Y., Taillard, E.: Parallel tabu search for real-time vehicle routing and dispatching. Transp. Sci. 33(4), 381–390 (1999)

    Article  MATH  Google Scholar 

  • Gonzales Hernandez, L.F., Corne, D.W.: Evolutionary divide and conquer for the set-covering problem. In: Lecture Notes in Computer Science, vol. 1143, pp. 198–208 (1996)

  • Hale, W.K.: Frequency assignment: Theory and applications. Proc. IEEE 68(12), 1497–1514 (1980)

    Article  Google Scholar 

  • Hellebrandt, M., Heller, H.: A new heuristic method for frequency assignment. Tech. Report TD(00) 003, COST259, Valencia, Spain (Jan. 2000)

  • Hurley, S., Smith, D.: Meta-heuristics and channel assignment. In: Hurley, S., Leese, R. (eds.) Methods and Algorithms for Radio Channel Assignment. Oxford University Press, Oxford (2002)

    Google Scholar 

  • Hurley, S., Smith, D., Thiel, S.U.: FASoft: A system for discrete channel frequency assignment. Radio Sci. 32(5), 1921–1939 (1997)

    Article  Google Scholar 

  • Gendron, B., Crainic, T.G.: Parallel branch-and-bound algorithms: Survey and synthesis. Oper. Res. 42(6), 1042–1066 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Karaoglu, N., Manderick, B.: FAPSTER—a genetic algorithm for frequency assignment problem. In: Proc. of the 2005 Genetic and Evolutionary Computation Conference, Washington D.C., USA, 2005

  • Karp, R.M.: Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane. Math. Oper. Res. 2(3), 209–224 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  • Koster, A.M.C.A., van Hoesel, C.P.M., Kolen, A.W.J.: Solving partial constraint satisfaction problems with tree decomposition. Networks 40(3), 170–180 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Kravets, V.L., Sergienko, I.V.: Decomposition method of solving a class of combinatorial optimization problems. Cybern. Syst. Anal. 19(6), 833–837 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • Mannino, C., Sassano, A.: An enumerative algorithm for the frequency assignment problem. Discrete Appl. Math. 129(1), 155–169 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Mannino, C., Oriolo, G., Ricci, F.: Solving stability problems on a superclass of interval graphs. T.R. n. 511, Vito Volterra (2002)

  • Montemanni, R., Moon, J.N., Smith, D.H.: An improved tabu search algorithm for the fixed-spectrum frequency-assignment problem. IEE Trans. Veh. Technol. 52(3), 891–901 (2003)

    Article  Google Scholar 

  • Pardalos, P., Rappe, J., Resende, M.: An exact parallel algorithm for the maximum clique problem. In: De Leone, P.P.R., Murl’i, A., Toraldo, G. (eds.) High Performance Algorithms and Software in Nonlinear Optimization. Kluwer, Dordrecht (1998)

    Google Scholar 

  • Pekny, J.F., Miller, D.L.: An exact parallel algorithm for the resource constrained traveling salesman problem with application to scheduling with an aggregate deadline. In: Proc. of the 1990 ACM Annual Conference on Cooperation, Washington, D.C., USA, 1990

  • Ralphs, T.K.: Parallel branch and cut for capacitated vehicle routing. Parallel Comput. 29(5), 607–629 (2003)

    Article  Google Scholar 

  • Schabauer, H., Schikuta, E., Weishaupl, T.: Solving very large traveling salesman problems by SOM parallelization on cluster architectures. In: Proc. of Sixth International Conference on the Parallel and Distributed Computing, Applications and Technologies, Vienna, Austria, 2005

  • Taillard, E.D.: Parallel iterative search methods for vehicle routing problems. Networks 23, 661–673 (1993)

    Article  MATH  Google Scholar 

  • Taillard, E.D.: Parallel taboo search techniques for the job shop scheduling problem. ORSA J. Comput. 6(2), 108–117 (1994)

    MATH  Google Scholar 

  • Talbi, E.G., Mostaghim, S., Okabe, T., Ishibuchi, H., Rudolph, G., Coello, C.A.: Parallel approaches for multiobjective optimization. In: Lecture Notes in Computer Science, vol. 5252, pp. 349–372 (2008)

  • Toulouse, M., Thulasiraman, K., Glover, F.: Multi-level cooperative search: a new paradigm for combinatorial optimization and an application to graph partitioning. In: Lecture Notes in Computer Science, vol. 1685, pp. 533–542 (1999)

  • Valenzuela, C.L., Jones, A.J.: Evolutionary divide and conquer (I): A novel genetic approach to the TSP. Evol. Comput. 1(4), 313–333 (1993)

    Article  Google Scholar 

  • van Dongen, S.: A cluster algorithm for graphs. Technical Report INS-R0010, National Research Institute for Mathematics and Computer Science in the Netherlands, Amsterdam (2000)

  • Walshaw, C.: A multilevel approach to the graph colouring problem. Tech. Rep. 01/IM/69, University of Greenwich, London (2001)

  • Zhang, Y.: Parallel algorithms for combinatorial search problems. Ph.D. Thesis, University of California at Berkeley (1989)

Download references

Author information

Authors and Affiliations

  1. Centre for Intelligent Network Design, School of Computer Science, Cardiff University, 5 The Parade, Roath, Cardiff, CF24 3AA, Wales, UK

    Gualtiero Colombo & Stuart M. Allen

Authors
  1. Gualtiero Colombo
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Stuart M. Allen
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Gualtiero Colombo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colombo, G., Allen, S.M. A comparison of problem decomposition techniques for the FAP. J Heuristics 16, 259–288 (2010). https://doi.org/10.1007/s10732-009-9116-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-009-9116-4